Low complexity affine MMSE detector for iterative detection-decoding MIMO OFDM systems

Iterative turbo processing between detection and decoding shows near-capacity performance on a multiple-antenna system. Combining iterative processing with optimum front-end detection is particularly challenging because the front-end maximum a posteriori (MAP) algorithm has a computational complexity that is exponential. Sub-optimum detector such as the soft interference cancellation linear minimum mean square error (SIC-LMMSE) detector with near front-end MAP performance has been proposed in the literature. The asymptotic computational complexity of SIC-LMMSE is O(n
_t

²
n
_r
+ n
_t
n
_r

³
+ n
_t
M
_c
2
^Mc
) per detection-decoding cycle where n
_t
is number of transmit antenna, nr is number of receive antenna, and Mc is modulation size. A lower complexity detector is the hard interference cancellation LMMSE (HIC-LMMSE) detector. HIC-LMMSE has asymptotic complexity of O(n
_t

²
n
_r
+ n
_t
M
_c
2
^Mc
) but suffers extra performance degradation. In this paper, two front-end detection algorithms are introduced that not only achieve asymptotic computational complexity of O(n
_t

²
n
_r
+ n
_t
n
_r

²
[Gamma (beta) + 1] + n
_t
M
_c
2
^Mc
) where Gamma(beta) is a function with discrete output {-1, 2, 3, ...,n
_t
} and O(n
_t
M
_c
2
^Mc
) respectively. Simulation results demonstrate that the proposed low complexity detection algorithms offer exactly same performance as their full complexity counterpart in an iterative receiver while being computational more efficient.